[Inquiry] Re: Prospects for Inquiry Driven Systems

[Jon Awbrey]

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PRO.  Note 7

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1.1.2.1.  Vector Field and Control System

Dynamically, in a control system, intelligence is a decision process
that selects an indicator of a tangent vector to follow at a point
or a descriptor of a corresponding operator to apply at that point.

The pointwise indicators or descriptors can be any relevant signs
or symbolic expressions:  address pointers, code numbers, names,
or quoted phrases.

A "vector field" is a construct that attaches to each point of
phase space a single tangent vector or differential operator.

A "control system" may be viewed as a ready generalization of a vector field,
in which whole sets of tangent vectors or differential operators are attached
to each point of phase space.

The "strategy" or "policy problem" of a controller is to pick out one of these
vectors to actualize at each point in accord with reaching a given target or
for the sake of satisfying a given property.

An individual control system is specified by the information that is attached
to each dynamic point, defining a subset of the tangent space at that point.
This pointwise subset is called "the indicatrix of permissible velocities"
by (Arnold, 1986, ch. 11).

In the form of usage that is needed for combining AI and control systems
to obtain autonomous intelligent systems, it is important to recognize
that the pointwise descriptors and indicators must eventually take on
the characters of symbolic expressions that exist in a language of
non-trivial complexity.  In relation to this purpose, it does not
really matter if their information is viewed as represented in
the states of discrete machines or in the states of physical
systems to which real and complex valued measurements are
attributed.  What makes the system of descriptions and
indications into a language is that its elements obey
specific sets of axioms that come to be recognized as
characterizing interesting classes of symbol systems.

Later on I will indicate one very broad definition of signs and symbol systems
that I favor.  I find that this conception of signs and languages equips the
discussion of intelligent systems with an indispensable handle on the levels
of complexity that arise in their description, analysis, and clarification.

Jon Awbrey

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